Data migration and integration system

ABSTRACT

A data migration and integration system is disclosed. In various embodiments, the system includes a memory configured to store a mapping from a source schema to a target schema; and a processor coupled to the memory and configured to migrate to a target schema an instance of source data organized according to the source schema, including by using a chase engine to perform an ordered sequence of steps comprising adding a bounded layer of new elements to a current canonical chase state associated with migrating the source data to the target schema; adding coincidences associated with one or more of the target schema data integrity constraints and a mapping from the source schema to the target schema; and merging equal elements based on the coincidences; and repeat the preceding ordered sequence of steps iteratively until an end condition is met.

CROSS REFERENCE TO OTHER APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/844,810, entitled DATA MIGRATION AND INTEGRATION SYSTEM filed Apr. 9,2020 which is incorporated herein by reference for all purposes, whichclaims priority to U.S. Provisional Application No. 62/832,214, entitledDATA MIGRATION AND INTEGRATION SYSTEM filed Apr. 10, 2019 which isincorporated herein by reference for all purposes.

GOVERNMENT LICENSE RIGHTS

This invention was made with government support under Small BusinessInnovation Research Program grant number 70NANB16H178, awarded by theNational Institute of Standards and Technology, U.S. Department ofCommerce. The government has certain rights in the invention.

BACKGROUND OF THE INVENTION

Data migration and integration systems have been provided toprogrammatically integrate data from separate databases into a singledatabase. However, typical approaches do not scale well to migrationand/or integration of very large data sets.

BRIEF DESCRIPTION OF THE DRAWINGS

Various embodiments of the invention are disclosed in the followingdetailed description and the accompanying drawings.

FIG. 1A is a block diagram illustrating an embodiment of a datamigration system.

FIG. 1B is a block diagram illustrating an embodiment of a datamigration system.

FIG. 2 is a flow chart illustrating an embodiment of a process tomigrate data.

FIG. 3 is a flow chart illustrating an embodiment of a process toperform a canonical chase step.

FIG. 4A illustrates an example of a data migration from a databaseinstance 402 according to a schema C to a target schema D 404 via amapping (functor) F 406.

FIG. 4B illustrates the data migration of FIG. 4A as sets of tables.

FIGS. 5A through 5C illustrate an example of using a chase engine asdisclosed herein to migrate data from schema C to schema D in variousembodiments.

DETAILED DESCRIPTION

The invention can be implemented in numerous ways, including as aprocess; an apparatus; a system; a composition of matter; a computerprogram product embodied on a computer readable storage medium; and/or aprocessor, such as a processor configured to execute instructions storedon and/or provided by a memory coupled to the processor. In thisspecification, these implementations, or any other form that theinvention may take, may be referred to as techniques. In general, theorder of the steps of disclosed processes may be altered within thescope of the invention. Unless stated otherwise, a component such as aprocessor or a memory described as being configured to perform a taskmay be implemented as a general component that is temporarily configuredto perform the task at a given time or a specific component that ismanufactured to perform the task. As used herein, the term ‘processor’refers to one or more devices, circuits, and/or processing coresconfigured to process data, such as computer program instructions.

A detailed description of one or more embodiments of the invention isprovided below along with accompanying figures that illustrate theprinciples of the invention. The invention is described in connectionwith such embodiments, but the invention is not limited to anyembodiment. The scope of the invention is limited only by the claims andthe invention encompasses numerous alternatives, modifications andequivalents. Numerous specific details are set forth in the followingdescription in order to provide a thorough understanding of theinvention. These details are provided for the purpose of example and theinvention may be practiced according to the claims without some or allof these specific details. For the purpose of clarity, technicalmaterial that is known in the technical fields related to the inventionhas not been described in detail so that the invention is notunnecessarily obscured.

Techniques to migrate and/or integrate large data sets are disclosed. Invarious embodiments, a data migration and integration system asdisclosed herein determines programmatically a mapping to integrate afirst database having a first schema into a second database having asecond schema, such as to merge one database into another and/or tootherwise combine two or more structured data sets.

In various embodiments, a data migration and integration system asdisclosed herein is configured to integrate data schema at least in partby computing left Kan extensions based on the “chase” algorithm fromrelational database theory. A breadth-first construction of an initialterm model for a particular finite-limit theory associated with eachleft Kan extension is performed.

In various embodiments, left-Kan extensions are computed as disclosedherein. In various embodiments, a chase engine configured to implement acanonical chase algorithm as disclosed herein is used.

In various embodiments, left Kan extensions are used for dataintegration purposes, as disclosed herein, including without limitationas illustrated by the following examples:

-   -   Functorial data migration based ETL tool. In various        embodiments, a CQL-based ETL tool is provided using techniques        disclosed herein.    -   Universal Data Warehousing. In various embodiments, a ‘universal        data warehousing’ design pattern provides an automated way to        create a data warehouse from schema and data matching inputs by        constructing colimits. These colimits are implemented in various        embodiments as left Kan extensions, as disclosed herein, to        perform data warehousing processes.    -   Meta catalog based on Semantic Search. In various embodiments,        techniques disclosed herein are applied to provide semantic        search capability (i.e., search guided by an ontology) across        manufacturing service suppliers. In various embodiments, left        Kan extensions are used to operate correctly.

In various embodiments, a data migration system as disclosed herein mayinclude a data migration engine, referred to as “chase engine” in someembodiments, which is configured to migrate data from a source database,in some embodiments structured according to a source schema, to a targetdatabase having a target schema.

In some embodiments, data migration is performed using a chase enginethat uses the chase algorithm from relational database theory to computeleft-Kan extensions of set-valued functors. The chase engine constructsan initial model of a particular finite-limit theory associated witheach left-Kan extension.

Left Kan extensions are used for many purposes in automated reasoning:to enumerate the elements of finitely-presented algebraic structuressuch as monoids; to construct semi-decision procedures for Thue(equational) systems; to compute the cosets of groups; to compute theorbits of a group action; to compute quotients of sets by equivalencerelations; and more.

Left Kan extensions are described category-theoretically. Let C and D becategories and F:C→D a functor. Given a functor J:D→Set, where D→Set(also written Set^(D)) is the category of functors from D to thecategory of sets, Set, we define Δ_(F) (J):C→Set:=J∘F, and think ofΔ_(F) as a functor from D→Set to C→Set. Δ_(F) has a left adjoint, whichcan be written as Σ_(F), taking functors in C→Set to functors in D→Set.Given a functor I:C→Set, the functor Σ_(F) (I):D→Set is called theleft-Kan extension of I along F.

Left Kan extensions always exist, up to unique isomorphism, but theyneed not be finite, (i.e., Σ_(F) (I)(d) may have infinite cardinalityfor some object d∈D, even when I (c) has finite cardinality for everyobject c∈C). In various embodiments, finite left-Kan extensions arecomputed when C, D, and F are finitely presented and I is finite.

In various embodiments, left-Kan extensions are used to perform datamigration, where C and D represent database schemas, F a “schemamapping” defining a translation from C to D, and I an input C-database(sometimes referred to as an “instance”) that is to be migrated to D.Typical previously-known left-Kan algorithms were impractical for largeinput instances, yet bore an operational resemblance to the chasealgorithm from relational database theory, which is also used to solvedata migration problems, and for which efficient implementations areknown. The chase takes a set of formulae F in a subset of first-orderlogic known to logicians as existential Horn logic, to categorytheorists as regular logic, to database theorists as embeddeddependencies, and to topologists as lifting problems, and constructs anF-model chase_(F)(I) that is weakly initial among other such “F-repairs”of I.

In various embodiments, an implementation of a chase algorithm is usedto compute a Left-Kan extension. In various embodiments, the chase, whenrestricted to the regular logic theories generated by left-Kan extensioncomputations (so-called finite-limit theories), constructs stronglyinitial repairs. In some embodiments, a chase-based left-Kan extensionalgorithm as disclosed herein is implemented as a scalable chase engines(software implementation of chase algorithm), which supports theentirety of finite-limit logic. In various embodiments, the algorithmand implementation thereof are part of the categorical query languageCQL, available at http://categoricaldata.net.

Various embodiments are described in connection with the accompanyingFigures as described below.

FIG. 1A is a block diagram illustrating an embodiment of a datamigration system. In the example shown, a data migration system 102receives source data 104, such as a set of files, one or more sourcedatabases, and/or other sources of data, such as streamed data. Invarious embodiments, data migration system 102 transforms the data andprovides the transformed data to a target data system 106 to be storedin a target database 108. In various embodiments, data migration system102 is configured to transform the data from data sources 104 accordingto a schema of the target database 108 and a mapping that defines therelationship between data and structures of the source data 104 tocorresponding entities and structures of the database 108.

In various embodiments, the transformation is performed at least in partusing an implementation of a chase algorithm is used to compute aLeft-Kan extension. In some embodiments, a data migration configured toimplement a canonical chase algorithm as disclosed herein is used.

FIG. 1B is a block diagram illustrating an embodiment of a datamigration system. In the example shown, data migration system 102 ofFIG. 1A is configured to migrate data from a source database 124 to atarget database 128. Data migration system 102 in this example is shownto include a data migration engine 132 configured to transform data fromsource database 124 according to a mapping 134 and to provide thetransformed data to target database 128.

In various embodiments, the mapping 134 comprises at least in part amapping expressed in a declarative language, such as the CategoricalQuery Language (CQL). In some embodiments, a migration tool is provided.Entities and structures from the source schema and the target schema arediscovered and presented for mapping. A user with knowledge of the dataand/or data domain uses the tool to identify and define mappings fromsource entities (data elements, relations, etc.) and structures (tables,etc.) to corresponding target entities and structures. The datamigration system 132 interprets the received mapping 134 and uses themapping to transform the source data to generate transformed data whichis then stored in the target database 128.

In various embodiments, the data migration engine 132 is configured totransform data at least in part using an implementation of a chasealgorithm is used to compute a Left-Kan extension. In some embodiments,a data migration configured to implement a canonical chase algorithm asdisclosed herein is used.

FIG. 2 is a flow chart illustrating an embodiment of a process tomigrate data. In various embodiments, the process 200 of FIG. 2 may beimplemented by a data migration system and/or engine, such as datamigration system 102 of FIGS. 1A and 1B and data migration engine 132 ofFIG. 1B. In the example shown, at step 202 data structures (e.g.,tables) according to the target schema are created and initialized to aninitial chase state. At step 204, an iteration of a set of ordered datamigration processing actions is performed. In various embodiments, theset of ordered data migration processing actions comprises a step oriteration of a canonical chase algorithm as disclosed herein. At step206, it is determined whether any further steps or actions are to beperformed. In various embodiments, a determination at step 206 that norfurther steps or actions are to be performed is based at least in parton a determination that no (further) action in the set of ordered datamigration processing actions performed in each iteration of step 204 isto be performed based on the current state of the “chase”. If no furthersteps or actions are to be performed (206), the process ends. If furthersteps or actions are to be performed (206), a next iteration of the setof ordered data migration processing actions is performed at step 204.Successive iterations of step 204 are performed until it is determinedat 206 that no further operations are to be performed, upon which theprocess ends.

FIG. 3 is a flow chart illustrating an embodiment of a process toperform a canonical chase step. In various embodiments, the process ofFIG. 3 comprises a set of ordered data migration processing actionsperformed to implement step 204 of FIG. 2 . In the example shown, at 302a single, bounded layer of new elements is added to a set of datastructures used to store a current chase state, sometimes referred toherein as “action α”. At 304, coincidences induced by target schema D(sometimes referred to as “action β_(D)”) are added to the chase state.In some embodiments, the term “adding coincidences” in the context ofdata migration may equate to “firing equality-generating dependencies”.At 306, coincidences induced by functor F that maps equivalences betweensource schema C and target schema D (sometimes referred to as “actionβ_(F)”) are added. At 308, all coincidences induced functionality(sometimes referred to as “action δ”) are added. At 310, coincidentallyequal elements are merged (sometimes referred to as (sometimes referredto as “action γ”). Finally, at 312 equivalences are reset in preparationfor a (potential) next iteration of the process of FIG. 3 (e.g., step204 of FIG. 2 ).

In various embodiments, steps 302, 304, 306, 308, 310, and 312 areperformed in the order shown in FIG. 3 .

Operation of the data migrations systems of FIGS. 1A and 1B and the datamigration processes of FIGS. 2 and 3 as implemented in variousembodiments as applied to a specific instance of a source data C to betransformed according to a mapping F to a target schema D is illustratedbelow with reference to FIGS. 4A, 4B, 5A, 5B, and 5C.

FIG. 4A illustrates an example of a data migration from a databaseinstance 402 according to a schema C to a target schema D 404 via amapping (functor) F 406. In various embodiments, techniques disclosedherein are used to migrate data from from C to D, as shown in FIG. 4A.

The example shown in FIG. 4A is a left-Kan extension that is an exampleof quotienting a set by an equivalence relation, where the equivalencerelation is induced by two given functions. In this example, the inputdata 402 consists of amphibians, land animals, and water animals, suchthat every amphibian is exactly one land animal and exactly one wateranimal. All of the animals (see 404) without double-counting theamphibians, which can be done by taking the disjoint union of the landanimals and the water animals and then equating the two occurrences ofeach amphibian.

As shown in FIG. 4A, source category C 402 is the spanLand′←Amphibian′→Water′, target category D 404 extends C into acommutative square with new object Animal and no prime (′) marks, andthe functor F 406 is the inclusion.

FIG. 4B illustrates the data migration of FIG. 4A as sets of tables.Specifically, input functor I:C→Set, displayed with one table perobject, is shown in FIG. 4B as tables 422, which in this example aremigrated to tables 424 (schema D) via mapping (functor) F 426. In tables422, frogs are double counted as both toads and newts, and the left-Kanextension (i.e., the table Amphibian′) equates them as animals.Similarly, geckos are both lizards and salamanders. Thus, one expect5+4−2=7 animals in Σ_(F) (I). However, there are infinitely manyleft-Kan extensions Σ_(F) (I); each is naturally isomorphic to thetables 424 of FIG. 4B in a unique way. That is, the tables 424 uniquelydefine Σ_(F) (I) up to choice of names.

Because in this example F is fully faithful, the natural transformationη_(I):I→Δ_(F) (Σ_(F) (I)), i.e. the unit of Σ_(F)┤Δ_(F) adjunction, isan identity of C-instances; it associates each source Land′ animal tothe same-named target Land animal, etc.

In various embodiments, the left-Kan extension ΣF (I):→Set of functorsF:C→D and I:C→Set is computed by using a chase engine to invoke a chasealgorithm on I and a theory col(F) associated with F, called the collageof F.

In various embodiments, left-Kan extensions are computed to perform datamigration using a chase engine in which that implements an algorithm inwhich each action corresponds to “firing of a dependency” in thetraditional sense of the chase. Because a chase algorithm to computeleft-Kan extensions as disclosed herein is completely deterministic andyields a result up to unique isomorphism, in some embodiments thealgorithm is referred to as the “canonical chase”.

In various embodiments, the input to the canonical chase as disclosedherein includes two finite presentations of categories, a finitepresentation of a functor, and a set-valued functor presented as afinite set of finite sets and functions between those sets. In someembodiments, such an input includes:

-   -   A finite set C, the elements of which we call source nodes.        -   For each c₁, c₂∈C, a finite set C (c₁, c₂), the elements of            which we call source edges from c₁ to c₂. We may write            f:c₁→c₂ or c₁→_(f) c₂ to indicate f∈C (c₁, c₂).    -   For each c₁, c₂∈C, a finite set C E(c₁, c₂) of pairs of paths        c₁→c₂, which we call source equations. By a path p:c₁→c₂ we mean        a (possibly 0-length) sequence of edges c₁→ . . . →c₂.    -   A finite set D, the elements of which we call target nodes.    -   For each d₁, d₂∈D, a finite set D(d₁, d₂), the elements of which        we call target edges from d₁ to d₂.    -   For each d₁, d₂∈D, a finite set D(d₁, d₂) of pairs of paths        d₁→d₂, which we call target equations.    -   A function F:C→D.    -   For each c₁, c₂∈C, a function Fc₁,c₂ from edges in C (c₁, c₂) to        paths F (c₁)→F (c₂) in D. We will usually drop the subscripts on        F when they are clear from context. We require that if p₁ and        p₂:c₁→c₂ are equivalent according to C E, the two paths F (p₁)        and F (p₂) are equivalent according to DE.    -   For each c∈C, a set I (c), the elements of which we call input        rows.    -   For each edge g:c₁→c₂∈C, a function I (c₁)→(c₂). Whenever paths        p₁ and p₂ are provably equal according to C E, we require that I        (p₁) and I (p₂) be equal as functions.

The above data determines category C (resp. D), whose objects are nodesin C (resp. D), and whose morphisms are equivalence classes of paths inC (resp. D), modulo the equivalence relation induced by C E (resp. DE).Similarly, the above data determines a functor F:C→D and a functorI:C→Set. In various embodiments, the source equations C E are not usedby a chase algorithm as disclosed herein, but are required to fullyspecify C.

In various embodiments, a canonical chase as disclosed herein runs inrounds, possibly forever, transforming a state consisting of a col(F)pre-model until a fixed point is reached (i.e., no more rules/actionsapply). In general, termination of the chase is undecidable, butconservative criteria exist based on the acyclicity of the “firingpattern” of the existential quantifiers 10] in the finite-limit theorycorresponding to DE described above. In various embodiments, the stateof a canonical chase algorithm as disclosed herein includes:

-   -   For each d∈D, a set J (d), the elements of which we call output        rows. J is initialized in the first round by setting J (d):=        _((c∈C|F(c)=d))I(c)    -   For each edge d∈D, an equivalence relation ˜_(d)⊆J (d)×J (d),        initialized to identity at the beginning of every round.    -   For each edge f:d1→d2∈D, a binary relation J (f)⊆J (d₁)×J (d₂),        initialized in the first round to empty. When the chase        completes, each such relation will be total and functional.    -   For each node c∈C, a function η(c):I (c)→J (F (c)). η is        initialized in the first round to the co-product/disjoint-union        injections from the first item, i.e., η(c)(x)=(c, x).

Given a path p:d₁→d₂ in D, we may evaluate p on any x∈J (d₁), writtenp(x), resulting in a (possibly empty) set of values from J (d₂) (a setbecause each J (f) is a relation). Given a state, we may consider it asa col(F) pre-model in the obvious way by extending ˜ into a congruence(e.g., so that x˜y and J (f)(x, a) implies J (f)(y, a)).

In various embodiments, a canonical chase algorithm as disclosed hereinconsists of a fully deterministic sequence of state transformations, upto unique isomorphism. In some embodiments, a chase algorithm asdisclosed herein comprises an equivalent sequence of transformations, insome embodiments executed in bulk.

A step of a canonical chase algorithm as implemented in variousembodiments comprises applying the actions below to the canonical chasestate in the order they appear in the following list:

-   -   Action α: add new elements. For every edge g:d₁→d₂ in D and x∈J        (d₁) for which there does not exist y∈J (d₂) with (x, y)∈J (g),        add a fresh (not occurring elsewhere) symbol g(x) to J (d₂), and        add (x, g(x)) to J (g), unless x was so added. Note that this        action may not force every edge to be total (which might lead to        an infinite chain of new element creations), but rather adds one        more “layer” of new elements.    -   Action β_(D): add all coincidences induced by D. The phrase “add        coincidences” is used where a database theorist would use the        phrase “fire equality-generating dependencies”. In this action,        for each equation p=q in DE(d₁, d₂) and x∈J (d₁), we update ˜d₂        to be the smallest equivalence relation also including {(x′,        x″)|x′∈p(x), x″∈q(x)}.    -   Action β_(F): add all coincidences induced by F. This action is        similar to the action above, except that the equation p=q comes        from the collage of F and evaluation requires data from η and I        in addition to J.    -   Action δ: add all coincidences induced functionality. For every        (x, y) and (x, y′) in J (f) for some f:d₁→d₂ in D with y≠y′,        update ˜d₂ to be the smallest equivalence relation also        including (y, y′). This step makes ˜ into a congruence, allowing        us to quotient by it in the next action.    -   Action γ: merge coincidentally equal elements. In many chase        algorithms, elements are equated in place, necessitating complex        reasoning and inducing non-determinism. In various embodiments,        a canonical chase algorithm as disclosed herein is        deterministic: action α adds a new layer of elements, and the        next action add to ˜. In this last action (γ), we replace every        entry in J and η with its equivalence class (or representative)        from ˜, and then ˜ resets on the next round.

FIGS. 5A through 5C illustrate an example of using a chase engine asdisclosed herein to migrate data from schema C to schema D in variousembodiments. In various embodiments, the example shown in FIGS. 5Athrough 5C illustrate application of a canonical chase algorithm asdisclosed herein to migrate the instance of C shown in FIGS. 4A and 4Bto the schema D.

In various embodiments, a data migration engine/system as disclosedherein begins by initializing the chase state, as in step 202 of FIG. 2, e.g., by creating tables or other data structures corresponding to thetarget schema and copying from the source data values for the firstcolumn of each table in the target schema for which corresponding dataexists in the source data. In some embodiments, auxiliary datastructures used in subsequent data migration processing steps andactions are initialized.

Comparing the source data tables 422 of FIG. 4B with the example initialchase state 500A shown in the upper part of FIG. 5A, one can see thatthe first column of each of the “Land”, “Water”, and “Amphibian” tableshas been populated with corresponding data from the corresponding sourcetables 422 in FIG. 4B.

Once the chase state has been initialized (500A of FIG. 5A), a single,bounded layer of new elements is added to the tables comprising thechase state, as in step 302 of FIG. 3 (action α). In variousembodiments, the target schema tables, data integrity constraints, andcurrent chase state are used to determine the bounded layer of elementsto be added. In the context of a left Kan extension, the target dataintegrity constraints include the equations in the target schema, aswell as the formulae in other logics (e.g. regular logic) derived fromthem. In the example shown in FIG. 5A, the target schema tables and dataintegrity constraints (e.g., “isLA”, “isWA”, “isAL”, and “isAW”), andthe current chase state (500A) are used to add elements, as shown inresulting chase state 500B.

In various embodiments, in each iteration of step 302 of FIG. 3 (actionα), a single layer of new elements is added to the chase state's “termmodel” in a “breadth first” way, i.e., once an element X is added thesystem does not add more things based on X in the current iteration ofthe action/step.

Next, coincidences (actions β_(D), β_(F), and δ, as in steps 304, 306,and 308 of FIG. 3 ) are added. In the example shown in FIGS. 5B, thesingle target equation in D induces no equivalences, because of themissing values (blank cells) in the isLA and isWA columns, so actionβ_(D) does not apply (because there are no values to which to apply theaction/rule). Action β_(F) requires that isAL and isAW be copies ofisAL′ and isAW′ (from the source schema C), inducing the equivalencesshown in box 502 of FIG. 5B. In this example, the relationscorresponding to the edges relations are all functions, so action δ doesnot apply. In a different example than the one shown, e.g., action δ mayforce element “a” and “b”: that are the same “water animal” to be thesame “animal”.

Next, coincidentally equally elements are merged (action γ, as in step310 of FIG. 3 ), resulting in the chase state transitioning from chasestate 500B (bottom of FIG. 5A and top of FIG. 5B) to chase state 500C asshown in FIG. 5B. In this example, the strike-through of the entries for“lizard” and “toad” in the Land table and “salamander” and “newt” in theWater table, resulting from the applicable equivalences 502, reflectsthose entries being subsumed into the identical entries that werealready present in those tables.

In this example, in the second and final round, no new elements areadded (i.e., there are no more elements to be migrated and no furtherrelations/constraints of the target schema that imply or requireadditional elements) and one action adds coincidences, β_(D). Inparticular, it induces the equivalences shown in boxes 504 of FIG. 5C:

-   -   isLA(lizard)˜isWA(salamander) isLA(toad)˜isWA(newt)        which, after merging, leads to a final state 500D as shown in        FIG. 5C.

The final chase state 500D shown in FIG. 5C is uniquely isomorphic tothe example output tables 424 shown in FIG. 4D. The actual choice ofnames in the tables 500D is not canonical but not unique, as one wouldexpect for a set-valued functor defined by a universal property, anddifferent naming strategies are used in various embodiments.

In various embodiments, a data migration engine/system as disclosedherein minimizes memory usage by storing cardinalities and lists insteadof sets. In some such embodiments, a left-Kan chase state consists of:

1. For each d∈ED, a number J(d)≥0 representing the cardinality of a set.

2. For each d∈ED, a union-find data structure based on path-compressedtrees ˜d⊆{n|0≤n<J(d)}×{n|0≤n<J(d)}.

3. For each edge ƒ:d1→d2∈D, a list of length J (d1), each element ofwhich is a set of numbers≥0 and <J(d2).

4. For each c∈C, a function η(c)→I(C)→{n|0≤n<J(F(c))}.

While a number of examples described above apply techniques describedherein to data migration/integration, in various embodiments techniquesdisclosed herein are applied to other contexts.

For example, and without limitation, in various embodiments techniquesdisclosed herein are used in various independent ‘operating/databasesystem’ embodiments as well as various independent ‘vertical/industryspecific’ embodiments, including without limitation one or more of thefollowing:

-   -   Isomorphism up to privacy/anonymity. The left Kan extension        concept is a purely structural one; it is not possible for CQL        or other data migrations systems to distinguish between        isomorphic instances. Such set-valued functors constructed by        Kan extension, including as done by CQL, have extremely pleasing        privacy properties, because by definition they contain no data        that could be leaked, period; they contain only structure (links        between meaningless identifiers). In various embodiments,        scalable databases with this property are enabled by wrapping        existing databases with CQL. For example, we can replace ‘Gecko’        with ‘1’ in the output of a left kan extension and still have a        left kan extension, thereby anonymizing Gecko and maintain the        Gecko's privacy    -   Automatic versioning. Left Kan extensions have suitable        semantics for schema evolution and they compose and have a right        adjoint; in various embodiments these attributes are used to        enable ‘automatic versioning’ of SQL systems by CQL schema        mappings and sigmas. The example in this disclosure can be        thought of as evolving the 3 table schema to have a fourth,        animals table.    -   Terms as Provenance. The ‘lineage’ of a data migration        formalized by a left Kan extension can be captured using terms.        Since left Kan extensions are universal in the sense of category        theory, provenance through Sigma is provided in various        embodiments. In this example, although the choice of names is        not unique, we can choose a naming scheme to encode how the name        is constructed, thereby preserving the provenance of each output        row.    -   Parallel Left Kan Computation. Although identities such as        Sigma_F(I+J)=Sigma_F(I)+Sigma_F(J) are known, computing Left Kan        extensions in parallel via parallel chase engines is disclosed,        enabling massive scalability of operations such as group orbit,        or coset enumeration, and initial term model construction for        algebraic theories.    -   Columnar/Skeletal storage. In various embodiments, the left Kan        extension algorithm as described herein makes use of a skeletal        storage strategy, where only cardinalities of sets, rather than        sets, are stored whenever possible. This strategy is related to        but distinct from the concept of virtual row numbers in columnar        databases. In various embodiments, columnar stores (MonetDB,        Vertica, etc), are optimized using theory about the “Skeleton”        of the category of sets.    -   Rapid creation of initial term models for algebraic theories is        enabled in various embodiments.

Embodiments of the present system are configured in some embodiments toprovide data integration services in divisible parts unrelated to thenumber of people using the system. Examples include offering integrationsolutions measured by types of integrations, number of integrations,size of integrations, complexity of integrations, duration ofintegration, permanence of integration, bandwidth required ofintegration, storage required of integration, processing power requiredof integration, and tools required to complete integration.

In various embodiments, the present system may be provided on onepremise or via a cloud infrastructure. The present system may beprovided via multiple cloud systems.

In some embodiments, the present system may include tools together orseparately. These may be configured via a SaaS platform or PaaSplatform. For example, the system may provide capabilities to deliverthe capabilities to manage the whole of the data integration task. Othermodules may include the ability to intake larger sized data sets orprocess the data integration more quickly. By utilizing the servicesprovided by a PaaS platform, other shared services may be included inthe deployment and pricing of the system.

In some embodiments, the present system may make available interactionsto the system through command line programming commands. In someembodiments the present system may allow for interactions to the systemthrough a Graphical User Interface (GUI).

In certain embodiments, functionality may include capabilities formanaging a suite of data integration projects including capabilities forprovisioning and managing storage and processing power.

In some embodiments, techniques disclosed herein are used to performdata integration functions or operations that present artifacts torepresent the state of data integrity. Data integration is presented asverifiable artifacts in some embodiments.

Illustrative embodiments integrate sets of data specific to individualdomains. Examples of domains include Energy, Transportation,Manufacturing, Logistics, Pharmaceuticals, Retail, Construction,Entertainment, Real Estate, Agriculture, Shipping, Security, Defense,Law, Health Care, Education, Tourism, and Finance.

A meta catalog may comprise a repository of ontologies acquired fromvarious industry domains. In various embodiments, acquisition of theseontologies are integrated with other ontologies.

In some embodiments, an ontology control interface uses ontologyacquired from one or more ontology sources. For each member Ø of the setof ontologies, operations are performed by the system to expose limitedObjects from one repository with one view. In the first operations ofthe system, the user selects the data objects to expose. Next, thesystem determines if the object may be transformed contemporaneous withexposure. If so, the system operation proceeds to provide additionalfunctions for transformation of the data prior to exposure.

In the following description, for the purposes of explanation, specificdetails are set forth in order to provide a thorough understanding ofembodiments of the invention. However, it can be apparent that variousembodiments may be practiced without these specific details.

In some embodiments, the systems may be configured as a distributedsystem where one or more components of the system are distributed acrossone or more target networks.

Larger integration projects can be created with verification ofsuccessful integration. This can allow for further integration of datawhile preserving ability to determine data provenance.

In various embodiments, ongoing improvements are leveraged through aversion control system with additional tools to track persons andrepresent the data state. Knowing the data state enables developers toimprove data prior to integration, working out errors and otherwisefixing difficulties in data cleanliness. Problems that may arise fromintegrations may then be followed up by determining provenance of dataand where in the larger system the flawed data may now be present.

In various embodiments, techniques disclosed herein may be used toperform data migration and similar operations efficiently andaccurately, without data or meta-information loss.

Although the foregoing embodiments have been described in some detailfor purposes of clarity of understanding, the invention is not limitedto the details provided. There are many alternative ways of implementingthe invention. The disclosed embodiments are illustrative and notrestrictive.

What is claimed is:
 1. A system, comprising: a memory configured tostore a mapping from a source schema of a source database comprisingsource data to a target schema of a target database to be populated withdesired target data, wherein the mapping comprises a left-Kan extensionrelationship between the source data and the desired target data; and aprocessor coupled to the memory and configured to migrate to the targetschema a database instance of the source schema, wherein the migrating,based on left-Kan extensions via the mapping to transform the sourcedata, is implemented at least in part by a chase engine executed on acomputer to invoke a chase algorithm to perform an ordered sequence ofsteps comprising: adding, based on one or more data integrityconstraints of the target schema, a bounded layer of new elements to thetarget data after a chase state has been initialized, wherein the chasestate iteratively approximates a desired left-Kan extension of thesource data according to the data integrity constraints in the targetschema; adding coincidences in the chase state based on the dataintegrity constraints of the target schema and the mapping from thesource schema to the target schema, wherein the coincidences are in partinduced by a functoriality that maps equal elements between the sourceschema to the target schema via the mapping; merging the equal elementsbased on the coincidences to output a final chase state that is uniquelyisomorphic to the desired left-Kan extension, wherein the final chasestate additionally contains a universal property of the desired left-Kanextension, the universal property comprising a data mapping from thesource data to target data; and repeating the ordered sequence of stepsiteratively until an end condition is met, wherein the end condition isbased at least in part on a determination that no further newcoincidences or new elements exist to be added.
 2. The system of claim1, wherein the mapping is expressed in a declarative language.
 3. Thesystem of claim 2, wherein the processor is configured to parse andinterpret the declarative language to determine and implement themapping.
 4. The system of claim 1, wherein the universal property of theleft-Kan extension comprises a unit of a sigma/delta adjunction.
 5. Thesystem of claim 1, wherein a coincidence is associated with anequivalency-adding dependency.
 6. The system of claim 1, wherein acoincidence is induced by the mapping.
 7. The system of claim 1, whereina coincidence is associated with an equivalence relation.
 8. The systemof claim 1, wherein the processor is further configured to initializecanonical chase state.
 9. A computer-implemented method, comprising:migrating, by a computer, to a target schema of a target database to bepopulated with desired target data a database instance of a sourceschema of a source database comprising source data, wherein themigrating is based on left-Kan extensions via a mapping to transform thesource data, wherein the mapping comprises a left-Kan extensionrelationship between the source data and the desired target data;creating and initializing, by a chase engine executed on the computer, achase state comprising an initial chase state of a set of data migrationdata structures according to the target schema; and performing, by thecomputer based on a chase algorithm, an ordered sequence of datamigration steps comprising: adding, based on one or more data integrityconstraints of the target schema, a bounded layer of new elements to thetarget data after the chase state has been initialized, wherein thechase state iteratively approximates a desired left-Kan extension of thesource data according to the data integrity constraints in the targetschema; adding coincidences in the chase state based on the dataintegrity constraints of the target schema and the mapping from thesource schema to the target schema, wherein the coincidences are in partinduced by a functoriality that maps equal elements between the sourceschema to the target schema via the mapping; merging the equal elementsbased on the coincidences to output a final chase state that is uniquelyisomorphic to the desired left-Kan extension, wherein the final chasestate additionally contains a universal property of the desired left-Kanextension, the universal property comprising a data mapping from thesource data to target data; and repeating the ordered sequence of stepsiteratively until an end condition is met, wherein the end condition isbased at least in part on a determination that no further newcoincidences or new elements exist to be added.
 10. The method of claim9, wherein the mapping is expressed in a declarative language.
 11. Themethod of claim 10, wherein the method further includes using aprocessor to parse and interpret the declarative language to determineand implement the mapping.
 12. The method of claim 9, wherein theuniversal property of the left-Kan extension comprises a unit of asigma/delta adjunction.
 13. The method of claim 9, wherein a coincidenceis associated with an equivalency-adding dependency.
 14. The method ofclaim 9, wherein a coincidence is induced by the mapping.
 15. The methodof claim 9, wherein a coincidence is associated with an equivalencerelation.
 16. A computer program product being embodied in anon-transitory computer readable medium and comprising computerinstructions executed on a computer to perform steps comprising:migrating to a target schema of a target database to be populated withdesired target data a database instance of a source schema of a sourcedatabase comprising source data, wherein the migrating is based onleft-Kan extensions via a mapping to transform the source data, whereinthe mapping comprises a left-Kan extension relationship between thesource data and the desired target data; creating and initializing, by achase engine, a chase state comprising an initial chase state of a setof data migration data structures according to the target schema; andperforming, by a chase algorithm, an ordered sequence of data migrationsteps comprising: adding, based on one or more data integrityconstraints of the target schema, a bounded layer of new elements to thetarget data after the chase state has been initialized, wherein thechase state iteratively approximates a desired left-Kan extension of thesource data according to the data integrity constraints in the targetschema; adding coincidences in the chase state based on the dataintegrity constraints of the target schema and the mapping from thesource schema to the target schema, wherein the coincidences are in partinduced by a functoriality that maps equal elements between the sourceschema to the target schema via the mapping; merging the equal elementsbased on the coincidences to output a final chase state that is uniquelyisomorphic to the desired left-Kan extension, wherein the final chasestate additionally contains a universal property of the desired left-Kanextension, the universal property comprising a data mapping from thesource data to target data; and repeating the ordered sequence of stepsiteratively until an end condition is met, wherein the end condition isbased at least in part on a determination that no further newcoincidences or new elements exist to be added.
 17. The computer programproduct of claim 16, wherein the mapping is expressed in a declarativelanguage.
 18. The computer program product of claim 17, furthercomprising computer instructions for using a processor to parse andinterpret the declarative language to determine and implement themapping.
 19. The computer program product of claim 16, wherein theuniversal property of the left-Kan extension comprises a unit of asigma/delta adjunction.